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NEW DEVELOPMENTS IN PRICE DYNAMICS²

Wage Dynamics: Reconciling Theory and Evidence

By AND LAWRENCE F. KATZ *

U.S. macroeconometric evidence shows a options (as opposed to match-speci®c negative relation between the rate of change productivity) in determination. of and the rate, con- (ii) In the light of this condition, we reinter- ditional on lagged price in¯ation. This pret the presence of an ``error correc- (wage) Phillips-curve relationship can be in- tion'' term in macroeconometric wage terpreted as a negative relation between the relations for most European economies expected rate of change of the real wage and but not in the . unemployment. (iii) We also show that whether this condition In contrast, most theories of the natural holds or not has important implications rate of unemployment imply what David for the effects of a number of variables, Blanch¯ower and Andrew Oswald (1994) from real rates to oil prices to have labeled a ``wage curve,'' that is, a neg- , on the natural rate of ative relation between the level of the real unemployment. wage and unemployment, given the reserva- tion wage and (if rent-sharing matters for I. The and the Wage Relation wage determination) the level of productivity. For example, models of unemployment based The relation between aggregate (annual) on ef®ciency wages, matching (or bargaining) time-series data on wage in¯ation, price in¯a- models, and competitive wage determination tion, and unemployment in the United States all generate such a wage-curve relation is reasonably well represented by a textbook (Blanchard and Katz, 1997). Phillips curve of the following form: How can one reconcile the empirical Phillips-curve relation and the theoretical (1) wtt0 w 0 1 Å awt/ (p 0 1 0 pt 0 2 ) wage-curve relation? In this paper, we address this question and make three main 0 butt/ ␧ points: where p and w are, respectively, the logarithms (i) We derive the condition under which one of the and nominal wage, u is the can go from the theoretical relation to a unemployment rate, aw is a constant, and ␧ is wage Phillips-curve speci®cation that an error term. The usual interpretation of this matches the U.S. empirical evidence. We equation is that the lagged in¯ation term (pt 0 1 0 show the constraints that such a condi- pt 0 2 ) proxies for expected current in¯ation e tion imposes on the determinants of (p t 0 pt 0 1 ). Under this interpretation, we can workers' reservation wages as well as the rewrite (1) to yield relative importance of workers' outside e (2) (wtt0 p ) Å a w/ (w t0 1 0 pt 0 1 )

² Discussants: , ; 0 butt/ ␧ . , . The macroeconomic empirical wage equation * Department of , Massachusetts Institute of Technology, Cambridge, MA 02139, and Department of implies that the (expected) log real wage de- Economics, , Cambridge, MA 02138, pends on the lagged log real wage (with a co- respectively. ef®cient of 1) and the unemployment rate. A low 69

/ 3y16 my11 Mp 69 Friday Nov 05 04:01 PM LP±AER my11 70 AEA PAPERS AND PROCEEDINGS MAY 1999 unemployment rate leads to an increase in the lagged wages. Much psychological re- expected real wage, and a high unemployment search, and fairness models of wage de- rate leads to a decrease in the expected real termination, also suggest that workers' wage. aspirations in search and wage bargain- Turn now to theory. Almost all theoretical ing are likely to be shaped by their previous models of wage-setting generate a strong core earnings. The reservation wage depends on implication: the tighter the labor market, the what the unemployed do with their time, higher is the real wage, given the workers' res- what is typically called the of leisure ervation wage. Most ef®ciency-wage or bar- but which also includes home production gaining models deliver a wage relation that can and earnings opportunities in the informal be represented (under some simplifying as- sector (the black and gray economies). A sumptions about functional form and the appro- plausible benchmark is that increases in priate indicator of labor-market tightness) as productivity in the informal and home pro- duction sectors are closely related to those e (3) (wtt0 p ) Å mb t/ (10 m)y t0 bu tt/ ␧ in the formal . The reser- vation wage ®nally depends on nonlabor in- where b is the log reservation wage and y is come. It also seems reasonable, at least with the log of labor productivity. The (expected) Harrod-neutral technological progress, for real wage depends on both the reservation productivity increases to lead to equal pro- wage (the wage equivalent of being unem- portional increases in labor and nonlabor ployed) and the level of productivity. The income. parameter m ranges from 0 to 1. In some Together, these factors suggest that the res- ef®ciency-wage models, such as the shirking ervation wage is likely to depend on both pro- model of and ductivity and lagged wages. The empirically (1984), productivity does not affect wages reasonable condition that technological pro- directly, so that m Å 1. In bargaining models gress does not lead to a persistent trend in the ( e.g., Dale Mortensen and Christopher unemployment rate puts an additional restric- Pissarides, 1994), m is typically less than 1 tion on this relation, namely, that the reserva- since wages depend on the surplus from a tion wage be homogeneous of degree 1 in the match and, thus, on productivity. real wage and productivity in the long run. Inspection of the empirical wage equation Rather than work with a general distributed lag (2) and the theoretical wage equation (3) relation, let us assume, for illustrative pur- shows two important differences. First, the poses, the following simple relation among the reservation wage and level of productivity en- reservation wage, the real wage, and the level ter (3) but not (2). Second, the Phillips curve of productivity: gives a relation between the change in the real wage and unemployment, whereas the theo- (4) bttÅ a / l(w 0 1 0 pt 0 1 ) / (1 0 l)yt retical model implies a relation between the level of the real wage (given the reservation where l is between 0 and 1. Substituting this wage and productivity) and unemployment. expression for the reservation wage into the These two distinctions are in fact intricately wage relation (3) and rewriting gives related. They point to the need to look at the e determinants of the reservation wage, to see (5) (wtt0 p ) Å ma / ml(w t0 1 0 pt 0 1 ) whether and when one can reconcile the two speci®cations. / (1 0 ml)yttt0 bu / ␧ . The reservation wage depends ®rst on the generosity of unemployment bene®ts and A comparison of equations (2) and (5) the other forms of income support individ- implies that the theoretical wage relation is uals can expect to receive if unemployed. consistent with the Phillips-curve represen- The institutional dependence of unemploy- tation if and only if ml Å 1. This can only ment bene®ts on previous wages suggests occur if two conditions are simultaneously that reservation wages will move with satis®ed:

/ 3y16 my11 Mp 70 Friday Nov 05 04:01 PM LP±AER my11 VOL. 89 NO. 2 NEW DEVELOPMENTS IN PRICE DYNAMICS 71

(i) There is no direct effect of productivity on Wage in¯ation depends not only on expected wages given the reservation wage (m Å 1). in¯ation and the unemployment rate, but also (ii) There is no direct effect of productivity on an error correction term, de®ned as the dif- on the reservation wage (l Å 1). ference between the lagged real wage and lagged labor productivity. That this is in gen- Both conditions are extreme but cannot be ruled eral a theoretically more appropriate speci®- out. For example, the Shapiro-Stiglitz ef®ciency- cation of the wage relation than the Phillips wage model, plus the assumption that the res- curve was a point ®rst made by J. D. Sargan ervation wage depends only on unemployment as early as 1964. Equations along the lines of bene®ts, which are in turn proportional to the (6) have since been estimated for various previous wage, yields both conditions. The OECD countries by a number of researchers strong performance of a standard wage Phillips- (e.g., OECD, 1997). curve speci®cation on U.S. data therefore These speci®cations differ in various ways, suggests that ml Å 1 may be a reasonable ap- in particular in their construction of labor pro- proximation for the United States.1 ductivity (trend or actual) and of expected in- ¯ation. For our purposes, however, they II. The United States versus Europe consistently yield one main conclusion. The coef®cient on the error correction term for the It has been known for some time that there is United States is close to zero with point esti- a striking difference between the empirical wage± mates that are typically wrong-signed (i.e., im- unemployment relations in the United States and plying a positive effect of the lagged real wage Europe. The difference, which might appear at adjusted for productivity on current wage in- ®rst to be rather esoteric, is the presence of an ¯ation), but small and insigni®cant. Put an- error correction term in the European but not in other way, the Phillips-curve speci®cation, the U.S. wage equation. Our discussion gives a which is nested in equation (6), appears to natural interpretation to this difference. provide a good description of the data. In most As a starting point, note that we can rewrite European countries, however, the error correc- equation (5) as tion term comes in with a signi®cant and right- signed coef®cient. On average, (1 0 ml)is (6) (wtt0 w 0 1 ) around 0.25. The discussion in the previous section pro- e Å ma / (p tt0 p 0 1 ) vides an interpretation of these ®ndings in terms of m and l. In the United States, both m and l are close to 1; in European countries, 0 (10 ml)(wt 0 1 0 pt 0 1 0 yt 0 1 ) either m or l or both are signi®cantly less / (10 ml)Dy 0 bu / ␧ . than 1. ttt This interpretation raises in turn three questions. First, how seriously should we take conclusions about m and l derived from 1 The speci®cation in equation (4) may be seen as im- estimation of aggregate relations? Second, posing too fast an adjustment of the reservation wage to why does it matter what the values of m and the real wage and to productivity. Our point goes through, however, for general speci®cations. The following exam- l might be? Third, what may explain the dif- ple is also of interest. Suppose that b follows a partial ferences in m and l across the two sides of adjustment process with respect to the real wage: bt Å a the Atlantic? We brie¯y take each one in / dbt 0 1 / (1 0 d)(wt 0 1 0 pt 0 1 ). Replacing in the wage turn. equation, assuming m Å 1, and rewriting gives

e (wtt0 w 1 ) Å a / (p tt0 p 1 ) 0 0 III. Micro versus Macro Data

0 b(utt0 du 0 1 ) / (␧tt0 d␧ 0 1 ). Thus, slow adjustment of the reservation wage implies the The macroeconomic data clearly support presence of a lagged term for unemployment (with a pos- a textbook wage Phillips-curve speci®ca- itive coef®cient), which is indeed a feature of U.S. data. tion for the United States and a modi®ed

/ 3y16 my11 Mp 71 Friday Nov 05 04:01 PM LP±AER my11 72 AEA PAPERS AND PROCEEDINGS MAY 1999 speci®cation with error correction but strong Katz, 1992).2 (This obviously does not im- autocorrelation of wages for OECD Europe. ply that the aggregate equation is correctly The possibility of strongly autocorrelated speci®ed or identi®ed; but this is another unobservables that affect wages has led some issue.) to argue that estimation using aggregate data may spuriously bias the effects of lagged IV. Implications for the Natural wages on current wages. Following this ar- Unemployment Rate gument, Blanch¯ower and Oswald (1994) have argued that micro (state or regional) Whether m and l are equal to or less than 1 data provide a more appropriate testing has important implications for the determina- ground for comparing Phillips-curve and tion of the natural rate of unemployment.3 Let wage-curve speci®cations. The typical em- us close our model of the labor market with pirical approach to comparing Phillips curves a simpli®ed ``price-setting'' or ``demand- and wage curves on state (or regional) data wage'' relation of the form has been to start from equation (5),toassume that the expected price in¯ation and produc- (8) wtttt0 p Å y 0 x tivity variables relevant for wage-setting are independent of the state and could thus be where x represents any factor that decreases captured by time dummies (dt ), and to run the wages ®rms can afford to pay (consistent with zero pro®ts for competitive product mar- (7) ws,tsÅ a / gw s,t 0 1 0 bus,tts/ d / ␧ ,t kets or an equilibrium markup for noncom- petitive product markets) conditional on the where s indexes state. Under these assump- level of technology. tions, the estimated of g will yield an Combining equations (5) and (8) and ig- e estimate of ml. noring expectational errors (replacingp t by One of the main conclusions reached by pt ) gives the equilibrium (natural) rate of un- Blanch¯ower and Oswald (1994) was that g , call it u t*: is indeed close to zero even in the United States. In other work (Blanchard and Katz, (9) u tt* Å (1ub) [ma 0 mlDy 1997), we have reexamined their evidence and concluded that the value of g one obtains from / Dxtt/ (1 0 ml)x 0 1 / ␧t ]. such an approach is in fact close to 1. (Similar conclusions have been reached by If we assume that both x and y are constant and Dean Hyslop [1997] for the United States and ␧ is equal to zero, this equation further and by Brian Bell [1996] for a number of other reduces to countries). A more important point is that this ap- (10) u* Å (1ub)[ma / (1 0 ml)x]. proach, at least with its reliance on time ®xed effects to capture aggregate variables, can- Thus, whether x has a permanent effect on the not give us a reliable estimate of ml. If one natural unemployment rate depends on relaxes the implicit assumption of no inter- whether ml is less than or equal to 1. If ml is state labor mobility that is typically implicit in estimates of (7), wages in a state are likely to depend not only on lagged state 2 wages, but also on the aggregate wage. In The approach is ®ne for asking about responses to state-speci®c shocks, but this is a different question from this case, the lagged aggregate wage effect responses to macro (national) shocks. Also, in principle will be hidden in the time ®xed effects, lead- the approach can be extended to answer the question at ing to a downward bias in estimates of g. hand by replacing time ®xed effects by explicit aggregate This source of bias is likely to be especially variables. But it then faces the same problems of speci®- cation as the aggregate wage equation. important for the United States, where labor 3 We therefore disagree on this point with the argu- mobility is a major source of adjustment to ments in recent papers by John Roberts (1997) and Karl state labor-market shocks (Blanchard and Whelan (1997).

/ 3y16 my11 Mp 72 Friday Nov 05 04:01 PM LP±AER my11 VOL. 89 NO. 2 NEW DEVELOPMENTS IN PRICE DYNAMICS 73 equal to 1, the level of x has no effect on the productivity of wages (1 0 m Å 0 for the natural rate. If ml is less than 1, the higher the United States, 1 0 m ú 0 in Europe), or to level of x, the higher is the natural rate. differences in (1 0 l), the direct effect of pro- Thus, if ml is indeed equal to 1 in the United ductivity on the reservation wage (1 0 l Å 0 States, but is less than 1 in Europe, this implies for the United States, 1 0 l ú 0 in Europe), that factors such as the level of energy prices, or both. interest rates, or payroll taxes will have no ef- With respect to m, the greater role of unions fect on the natural rate in the United States but in wage-setting and more stringent hiring and will have an effect on the natural rate in Eu- ®ring regulations in Europe could play a role rope. Given the large movements in these vari- in these differences in wage-setting behavior. ables over the last three decades, this is clearly Suggestive evidence of a greater direct effect a crucial difference between the two labor of ®rm productivity on wages in Europe than markets. in the United States comes from John Abowd There is another issue for which the exact et al.'s (1998) comparisons of wage-setting in speci®cation of the wage relation and the val- and the United States using comparable ues of m and l have potentially important im- matched employer±employee longitudinal plications, namely, the implications for the data.4 They ®nd much stronger positive effects relation between in¯ation and unemployment of productivity, capital intensity, and pro®t- (when the wage and the price relations are ability on establishment wage differentials, combined). We want to mention it although conditional on worker characteristics, in we have only limited progress in solving it. France than in the United States. Much of the recent empirical work in macro- With respect to l, the role of the under- economics has built on the work of John ground economy for the unemployed in many Taylor (1980). In the standard speci®cation, continental European economies may also be the wage is set equal to the average desired signi®cant. However, we are not aware of di- wage over the duration of a labor contract; the rect evidence on this point. desired wage is then a function of the price Overall, our analysis indicates the im- level and the unemployment rate. Importantly, portance of a better understanding of the de- for our purposes, the reservation wage is im- terminants of reservation wages and of the plicitly held constant. This line of research has importance of ®rm-speci®c rents as opposed run into an empirical problem (see Jeff Fuhrer to external labor-market conditions in wage- and George Moore [1995] for a discussion): setting in both Europe and the United States. it implies little or no direct dependence of in- ¯ation on lagged in¯ation. This is in contrast REFERENCES to the reduced-form evidence, which suggests a relation among the in¯ation rate, the lagged Abowd, John; Kramarz, Francis; Margolis, David in¯ation rate with a coef®cient equal to 1, and and Troske, Kenneth. ``The Relative Impor- the unemployment rate. We suspect that taking tance of Employer and Employee Effects on into account the dependence of the reservation Compensation: A Comparison of France wage on past wages holds a key to understand- and the United States.'' Mimeo, Cornell ing the dependence of in¯ation on itself University, 1998. lagged. But we have not established it yet. Bell, Brian. ``Wage Curve or Phillips Curve?'' Mimeo, Nuf®eld College, Oxford, U.K., V. What Explains the Difference Between September 1996. Europe and the United States? Blanchard, Olivier and Katz, Lawrence. ``Re- gional Fluctuations.'' Brookings Papers on To summarize, the macro evidence clearly Economic Activity, 1992, (1), pp. 1±61. indicates a lack of an error correction term in the United States and substantial error correc- 4 For our purposes, however, we care not only about tion effects for OECD Europe. Our conceptual the effect of ®rm productivity, but also about the effects framework attributes these differences either of sectoral and aggregate productivity on wages. The last to differences in (1 0 m), the direct effect of two effects are not identi®ed in Abowd et al.'s study.

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